Write an equation for the line tangent to the circle x^2 + y^2 = 17, at the point (4, 1). Enter your answer in slope-intercept form: y = mx + b; example: y = -5x-2

Question

zzr0ck3r · Answer

so you want to take the derivative of the equation of the circle and then that will give the slope

$x^2+y^2=17\implies 2x+2y\frac{dy}{dx}=0\\frac{dy}{dx}=\frac{-x}{y}$
so at the point $(4,1)$ the slope is $-4$

so your line will be of the form $$\large y=-4x+b$$

now use the point $(4,1)$ to find the value of b

note we know that the tangent line touches the circle at $(4,1)$ so we know that point is also on our line.

anonymous · Answer

So 17?

anonymous · Answer

for the value of B ?

anonymous · Answer

@zzr0ck3r :o

zzr0ck3r · Answer

how did you get 17?

anonymous · Answer

Idk :/ I plugged in 4 for x and 1 for y

zzr0ck3r · Answer

yes you are right im sorry its early lol

anonymous · Answer

Omg don't be sorry thanks for starting me off, I was struggling with this. thank you so much:)